Related papers: Adelic Model of Harmonic Oscillator
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for…
We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of cannonical commutation relations. We also discuss…
By using Supersymmetric Quantum Mechanics and Semiclassical Quantization, one may argue that the low-lying excited states of any quantum system can be modeled by a set of harmonic oscillators. In the present paper, we fit the experimental…
We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…
Two quantum quartic anharmonic many-body oscillators are introduced. One of them is the celebrated Calogero model (rational $A_n$ model) modified by quartic anharmonic two-body interactions which support the same symmetry as the Calogero…
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…
We consider a Generalized Uncertainty Principle (GUP) framework which predicts a maximal uncertainty in momentum and minimal uncertainties both in position and momentum. We apply supersymmetric quantum mechanics method and the shape…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
An unusual type of the exact solvability is reported. It is exemplified by the Coulomb plus harmonic oscillator in D dimensions after a complexification of its Hamiltonian which keeps the energies real. Infinitely many bound states are…
This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the…
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a…